Details

Degeneracy loci of Poisson varieties

by
Brent Pym
|
University of Toronto
Time: 14:10 (Monday, Sep. 19, 2011)Location: BA6183, Bahen Center, 40 St. George St.Abstract:
The degeneracy loci of a vector bundle morphism on an algebraic variety (that is, the loci where the rank of the fibrewise linear map drops) are well-studied objects in algebraic geometry. In particular, there are lower bounds on their dimensions, and for morphisms which are appropriately "generic", these bounds become equalities. However, if we instead restrict our attention to a special class of morphisms---for example, the solutions of some PDE---then the theory, as it stands, has little to say. In this talk, we will examine the case of a Poisson bivector field and find an impressive departure from the "generic" situation: the degeneracy loci are much bigger than expected in the classical theory! The explanation of this phenomenon is intimately related to some new aspects of Poisson module theory. This is joint work with Marco Gualtieri.